Statistics

Confidence Interval Calculator

Calculate the confidence interval for a population mean or proportion from sample data.

Inputs

Type

Sample Mean / Proportion (x̄ or p̂)

Standard Deviation (σ) or — for proportion

Sample Size (n)

Confidence Level

Results

—

Confidence Interval

Lower Bound—

Upper Bound—

Margin of Error—

Standard Error—

Confidence Intervals Explained

A 95% CI means: if we repeated the sampling 100 times, 95 of the intervals would contain the true population parameter. Formula: CI = x̄ ± Z × (σ/√n). A wider interval means less precision. Increase n to narrow the interval.

What is the Confidence Interval Calculator?

The Confidence Interval Calculator is an advanced statistics tool. Because you can rarely survey an entire population, this tool calculates a "range of values" from a sample that is highly likely to contain the true population mean.

How It Works (Formula)

The calculator determines the Margin of Error by multiplying the standard error of the mean by a Z-score (or T-score) associated with your desired confidence level (like 95%). It then adds and subtracts this margin from the sample mean.

$$ \text{CI} = \bar{x} \pm Z \left( \frac{s}{\sqrt{n}} \right) $$

The formula for finding the upper and lower bounds of the interval.

How to Use It

Enter your Sample Mean, Sample Size ($n$), and Standard Deviation. Then, choose your Confidence Level from the dropdown (usually 95% or 99%). The calculator will compute the Margin of Error and output your interval range.